Gradient-based approach to sample-time mismatch error calibration in a two-channel time-interleaved analog-to-digital converter

ABSTRACT

Correcting phase error in a two-channel TIADC system in a manner that is independent of the Nyquist zone(s) occupied by the input signal. In the preferred approach this is done using the gradient of a phase error estimate. The gradient may be determined from a simplified expression of linear regression; the direction of the adaptation is then controlled by the sign of the gradient. The adaptive algorithm converges to the optimal value regardless of the Nyquist zone occupied by the input signal.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application claims the benefit of U.S. Provisional Application Ser.No. 61/480,696 filed Apr. 29, 2011 entitled “Gradient-Based Approach toSample-Time Mismatch Error Calibration in a Two-Channel Time InterleavedAnalog-to-Digital Converter.” The entire contents of theabove-referenced application are hereby incorporated by reference.

BACKGROUND

Time-interleaved Analog-to-Digital Converters (TIADC) have receivedconsiderable attention in the recent past in applications that requirevery high sample rates, i.e., sample rates that cannot be achieved by asingle present-day ADC. In a TIADC employing M ADCs, each ADC operatesat F_(S)/M where F_(S) is the sampling rate of the TIADC. The outputfrom each TIADC is combined at F_(S) using a commutator to produce asample rate converter operating at F_(S). Ideally, the slower ADCsshould have the same offset, gain, and uniform sample instants. Inpractice, however, due to component mismatches, this requirement isdifficult to achieve. The differences in the offset values of the slowerADCs produce tones at kF_(S)/M, for k=0, 1, 2, . . . , irrespective ofthe input signal. The differences in the gain values of the ADCs producespurious (or unwanted) signals at ±F_(in)+kF_(S)/M, for k=1, 2, . . . ,where F_(in) is any frequency of the input signal. Similarly, thenon-uniformity of sampling instants of each ADC with respect to theTIADC sampling frequency produce spurious signals at exactly the samelocation as the spurs due to gain mismatch. However, the spurs due tothe sample-time mismatch are orthogonal to those due to the gainmismatch. Consequently, the resulting spurious signals due to offset,gain and sample-time mismatches degrade the performance of the TIADCsystem significantly, thus making the estimation and correction of theseerrors imperative to improve performance.

SUMMARY

In a preferred embodiment, phase error is corrected in a two-channelTIADC system in a manner that is independent of the Nyquist zone(s)occupied by an input signal. The input signal is first converted withtwo Time-Interleaved Analog to Digital Converters (TIADC) cores, toprovide to a set of two ADC outputs as first and second digital signals.The outputs of the TIADC cores are interleaved to form a digitalconverted representation of the input signal. A sample time error (alsoreferred to as a phase error) is then estimated from the first andsecond digital signals. The phase correction is then carried out usingthe phase error estimate, irrespective of a Nyquist zone occupied by theinput signal. The correction signal is then applied to a sample timecorrection input of at least one of the TIADC cores.

In one implementation, the correction signal is determined from a signof the gradient of the sample time error. The sign of the gradient ofthe sample time error may be further processed by a filter, such as aFinite Impulse Response filter, before applying it to the phasecorrection input.

The approach lends itself to a mixed signal solution such that the phaseerror estimate can be determined digitally, but the correction signalstill applied as an analog value output as from a Phase Look Up Table(PLUT). In a specific implementation, the correction signal isdetermined from a Phase Look Up Table (PLUT) where

PLUT^(k) = N_(i) + ⌊μ^(k)⌋μ^(k + 1) = μ^(k) − sign(e_(phase)^(k)(Δ t))  sign(m_(s)^(k))μ_(phase)^(k)$\begin{matrix}{\mu_{phase}^{k + 1} = {{\max( {\frac{\mu_{phase}^{k}}{2},\mu_{phasemin}} )}\mspace{14mu} {if}\mspace{14mu} {mod}\mspace{14mu} ( {k,k_{p}} )}} \\{= 0}\end{matrix}$

where N_(i) is an initial address offset of the PLUT, μ^(k) denotes avariable at the k^(th) iteration, and μ_(phase) ^(k) denotes a step sizeat the k^(th) iteration, μ_(phase) ⁰=μ_(phasemax), k_(p) is anyarbitrary positive number, and e_(phase)(Δt_(k)) is an estimate of thephase error at iteration k.

Any of several known algorithms to provide the initial estimate of thephase error can be used. One such sample-time error estimator wasdisclosed in U.S. Pat. No. 7,839,323 entitled “Error Estimation andCorrection in a Two-Channel Time Interleaved Analog to DigitalConverter”, filed Apr. 7, 2009, which is hereby incorporated byreference in its entirety. Other mismatch error correction algorithmsmay also be used, however.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing will be apparent from the following more particulardescription of example embodiments of the invention, as illustrated inthe accompanying drawings in which like reference characters refer tothe same parts throughout the different views. The drawings are notnecessarily to scale, emphasis instead being placed upon illustratingembodiments of the present invention.

FIG. 1 illustrates a spectrum of an input signal occupying a firstNyquist zone.

FIG. 2 illustrates variation of e_(phase)(Δt) with Δt for the inputsignal illustrated in FIG. 1.

FIG. 3 illustrates a spectrum of an input signal occupying a secondNyquist zone.

FIG. 4 illustrates variation of e_(phase)(Δt) with Δt for the signalshown in FIG. 3.

FIG. 5 is a schematic of a Two-Channel Time Interleaved of sample-timemismatch correction.

FIG. 6 illustrates a block diagram of an adaptive phase error algorithm.

FIG. 7 illustrates variation of PLUT^(k) with iteration k when the inputsignal is in the first Nyquist zone.

FIG. 8 illustrates variation of PLUT^(k) with iteration k when the inputsignal is in the second Nyquist zone.

FIG. 9 illustrates variation of PLUT^(k) with iteration k when the inputsignal switches between first and second Nyquist zones.

FIG. 10 illustrates use of the TIADC in a digital transceiver.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT

A description of example embodiments follows. While the invention isdefined solely by the claims presented at the end of this document andtherefore may be susceptible to embodiment in different forms, there isshown in the drawings, and will be described herein in detail, one ormore specific embodiments, with the understanding that the presentdisclosure is to be considered but one exemplification of the principlesof the invention. It is also to be understood that there is no intent tolimit the invention to that which is specifically illustrated anddescribed herein. Therefore, any references to the “invention” which mayoccur in this document are to be interpreted only as a reference to oneparticular example embodiment of but one aspect of the invention(s)claimed.

A Time-Interleaved Analog-to-Digital Converter (TIADC) employs multipleanalog-to-digital converters (ADCs) to achieve high sampling rates.Thus, in a TIADC employing M such ADCs, each ADC operates at F_(S)/Mwhere F_(S) is the sampling rate of the TIADC. Ideally, the slower ADCsshould have the same offset, gain, and uniform sample instants. Inpractice, however, due to component mismatches, this requirement isdifficult to achieve. The differences in the offset values of the slowerADCs produce tones at kF_(S)/M, for k=0, 1, 2, . . . , irrespective ofthe input signal. The differences in the gain values of the ADCs producespurious (or unwanted) signals at ±F_(in)+kF_(S)/M, for k=1, 2, . . . ,where F_(in) is any frequency of the input signal. Similarly, thenon-uniformity of sampling instants of each ADC with respect to theTIADC sampling frequency produce spurious signals at exactly the samelocation as the spurs due to gain mismatch. However, the spurs due tothe sample-time mismatch are orthogonal to those due to the gainmismatch. Consequently, the resulting spurious signals due to offset,gain and sample-time mismatches degrade the performance of the TIADCsystem significantly, thus making the estimation and correction of theseerrors imperative to improve performance.

Here the focus is on a two-channel TIADC system wherein the sample-time(also referred to herein as phase) mismatch error is estimated andcorrected. Expressions for the phase error have been developed whereinit is shown that the phase error produces image spurs reflected aroundthe Nyquist frequency. In developing expressions for the phase error, itis assumed that the gain and offset mismatch errors have been corrected.For the sake of exposition, the relevant expressions are developed for asingle sinusoidal input signal. It is also shown that the amplitude ofthis tone is commensurate with the amount of the phase error.

The expression for the phase error involves the cross-correlationbetween the two ADCs which is related to the phase mismatch between thetwo ADCs. It will be shown that the phase error depends on the Nyquistzone of the input signal. For instance, if the signal is in the firstNyquist zone, the slope of the phase error could be positive (negative)while the slope becomes negative (positive) when the signal occupies thesecond Nyquist zone. In applications where the input spectrum occupiesdifferent Nyquist zones at various time instants, the phase error slopetoggles between negative and positive values. Consequently, anyadaptation that is designed for a certain phase error slope tends todiverge when the sign of the phase error slope changes.

Here is presented an algorithm for phase correction that estimates theslope of the phase error continuously and accordingly changes thedirection of adaptation of the algorithm. While the adaptive algorithmis essentially based on the sign of the phase error, the sense ofadaptation is based on the sign of the slope estimate of the phaseerror. In other words, if the adaptive algorithm follows one directionof movement when the phase error slope is positive, it can be made tomove in the opposite direction when the phase error slope is negative.In this way, the adaptive algorithm will always converge irrespective ofthe Nyquist zone of the input signal. The input signal to thetwo-channel TIADC system is itself the training signal and theestimation and correction of the phase error is carried out in thebackground. In other words, the adaptation is performed using a blindadaptive technique. The entire adaptation is, in a preferred embodiment,a mixed-signal process wherein the estimation of the phase error iscarried out in the digital domain while the correction is carried out inthe analog domain. Without loss of generality, assume that theestimation information in the digital domain is transferred to anappropriate correction in the analog domain by way of a look-up table(LUT). In the adaptation loop, for instance, a certain address to theLUT is calculated based on the phase error, in conjunction with theslope of the phase error, and the value corresponding to that address inthe LUT is used in an appropriate analog circuit in the two-channelTIADC system to effect the correction.

Phase Error Correction

In this section, a two-channel TIADC system is considered with phaseerror only. It is assumed that the gain and phase mismatch errors havebeen corrected. Additionally, an input signal is assumed of the formx(t)=cos(2πF_(i)t+φ), where F_(i) is an arbitrary input frequency and φis an arbitrary phase.

The output of the two-channel TIADC system is given by

$\begin{matrix}{{y(n)} = \{ \begin{matrix}{\cos \mspace{14mu} ( {{2\pi \; F_{i}{nT}} + \varphi} )} & {n = {even}} \\{\cos \mspace{14mu} ( {{2\pi \; F_{i}{nT}} + {\Delta \; t} + \varphi} )} & {n = {odd}}\end{matrix} } & (1)\end{matrix}$

where T=1/F_(S) and F_(S) is the sampling frequency of the two-channelTIADC system. Combining the even and odd time instants in the aboveequation,

$\begin{matrix}{{y(n)} = {\cos \mspace{14mu} ( {{2\pi \; {F_{i}\lbrack {{nT} + \frac{\Delta \; t}{2} - {( {- 1} )^{2}\frac{\Delta \; t}{2}}} \rbrack}} + \varphi} )}} & (2)\end{matrix}$

Assume that the outputs corresponding to even time instants are outputfrom ADC1 while those corresponding to odd time instants are output fromADC2. In other words, ADC1 samples the input signal at time instants 2nTwhile ADC2 samples the input signal at time instants (2n+1)T+Δt.Consequently, Δt is the sample-time error. It should be mentioned thatthere is no loss of generality in grouping the total phase in one of theoutputs.

The above equation (2) can thus be expanded as

$\begin{matrix}{{y(n)} = {{\cos \mspace{14mu} ( {{2\pi \; {F_{i}\lbrack {{nT} + \frac{\Delta \; t}{2}} \rbrack}} + \varphi} )\mspace{14mu} \cos \mspace{14mu} ( {( {- 1} )^{n}\pi \; F_{i}\Delta \; t} )} + {\sin \mspace{14mu} ( {{2\pi \; {F_{i}\lbrack {{nT} + \frac{\Delta \; t}{2}} \rbrack}} + \varphi} )\mspace{14mu} \sin \mspace{14mu} ( {( {- 1} )^{n}\pi \; F_{i}\Delta \; t} )}}} & (3)\end{matrix}$

It can be seen that cos((−1)^(n)πF_(i)Δt)=cos(πF_(i)Δt). Since sin( ) isan odd function, with (−1)^(n)=cos(nπ), thensin((−1)^(n)πF_(i)Δt)=cos(nπ)sin(πF_(i)Δt). Usingsin(a)cos(nπ)=sin(a−nπ) and nπ=πF_(S)nT, the above equation can bewritten as

$\begin{matrix}\begin{matrix}{{y(n)} =} & {{{\cos \mspace{14mu} ( {\pi \; F_{i}\Delta \; t} )\mspace{14mu} \cos \mspace{14mu} ( {{2\pi \; F_{i}{nT}} + {\pi \; F_{i}\Delta \; t} + \varphi} )} +}} \\ & {{\sin \mspace{14mu} ( {\pi \; F_{i}\Delta \; t} )\mspace{14mu} \sin \mspace{14mu} ( {{2\pi \; F_{i}{nT}} + {\pi \; F_{i}\Delta \; t} - {\pi \; F_{s}{nT}} + \varphi} )}} \\{=} & {{{\cos \mspace{14mu} ( {\pi \; F_{i}\Delta \; t} )\mspace{14mu} \cos \mspace{14mu} ( {{2\pi \; F_{i}{nT}} + {\pi \; F_{i}\Delta \; t} + \varphi} )} +}} \\ & {{\sin \mspace{14mu} ( {\pi \; F_{i}\Delta \; t} )\mspace{14mu} \sin \mspace{14mu} ( {{( {{2\pi \; F_{i}} - {\pi \; F_{s}}} ){nT}} + {\pi \; F_{i}\Delta \; t} + \varphi} )}}\end{matrix} & (4)\end{matrix}$

Assuming that Δt is very small compared to T, cos(πF_(i)Δt)≈1 andsin(πF_(i)Δt)≈πF_(i)Δt. Consequently,

$\begin{matrix}\begin{matrix}{{y(n)} \approx} & {{{\cos \mspace{14mu} ( {{2\pi \; F_{i}{nT}} + {\pi \; F_{i}\Delta \; t} + \varphi} )} +}} \\ & {{( {\pi \; F_{i}\Delta \; t} )\mspace{14mu} \sin \mspace{14mu} ( {{( {{2\pi \; F_{i}} - {\pi \; F_{s}}} ){nT}} + {\pi \; F_{i}\Delta \; t} + \varphi} )}} \\{\approx} & {\underset{\underset{Input}{}}{\cos \mspace{14mu} ( {{2\pi \; F_{i}{nT}} + {\pi \; F_{i}\Delta \; t} + \varphi} )}}\end{matrix} & (5) \\{\mspace{50mu} {- \mspace{20mu} \underset{\underset{Image}{}}{( {\pi \; F_{i}\Delta \; t} )\mspace{14mu} \sin \mspace{14mu} ( {{( {{\pi \; F_{s}} - {2\pi \; F_{i}}} ){nT}} - {\pi \; F_{i}\Delta \; t} - \varphi} )}}} & (6)\end{matrix}$

It can now be seen from the above equation that the phase error producesan image tone with an amplitude proportional to the sample mismatchtiming Δt.

As is well known, a correlation between two sequences providesinformation about the time delay between them. Towards this end, definetwo sequences, y₁(n) and y₂(n), as the outputs from ADC1 and ADC2,respectively. Consequently

y ₁(n)=y(2n)  (7)

y ₂(n)=y(2n+1)  (8)

Now define a phase error as a function of the timing mismatch as

$\begin{matrix}\begin{matrix}{{e_{phase}( {\Delta \; t} )} =} & {{\frac{1}{N}{\sum\limits_{k = 1}^{N - 1}\; \{ {{{y_{1}( {n - 1 - k} )}{y_{z}( {n - 1 - k} )}} -} }}} \\ &  {{y_{2}( {n - 1 - k} )}{y_{1}( {n - k} )}} \} \\{=} & {{\frac{1}{N}{\sum\limits_{k = 1}^{N - 1}\; {{y_{2}( {n - 1 - k} )}\{ {{y_{1}( {n - 1 - k} )} - {y_{1}( {n - k} )}} \}}}}}\end{matrix} & (9)\end{matrix}$

where N is the number of samples from both ADCs used in the evaluationof e_(phase)(Δt). The above equation can also be written as

$\begin{matrix}\begin{matrix}{{e_{phase}( {\Delta \; t} )} =} & {{\frac{1}{N}{\sum\limits_{k = 0}^{N - 2}\; \{ {{y_{1}( {n - k} )}{y_{2}( {n - k} )}{y_{1}( {n - 1 - k} )}} \}}}} \\{=} & {{\frac{1}{N}{\sum\limits_{k = 0}^{N - 2}\; {{y_{2}( {n - k} )}\{ {{y_{1}( {n - k} )} - {y_{1}( {n - 1 - k} )}} \}}}}}\end{matrix} & (10)\end{matrix}$

An alternative expression for the phase error given by

$\begin{matrix}\begin{matrix}{{e_{{phase}\;}( {\Delta \; t} )} =} & {{{\frac{1}{N}{\sum\limits_{k = 1}^{N - 1}\; \{ {{y_{1}( {n - 1 - k} )} - {y_{2}( {n - 1 - k} )}} \}^{2}}} -}} \\ & {\{ {{y_{2}( {n - 1 - k} )} - {y_{1}( {n - k} )}} \}^{2}}\end{matrix} & (11)\end{matrix}$

also provides information about the phase error between the two ADCs.Again Eqn 11 can also be written as

$\begin{matrix}\begin{matrix}{{e_{phase}( {\Delta \; t} )} =} & {{{\frac{1}{N}{\sum\limits_{k = 0}^{N - 2}\; \{ {{y_{1}( {n - k} )} - {y_{2}( {n - k} )}} \}^{2}}} -}} \\\; & {\{ {{y_{2}( {n - k} )} - {y_{1}( {n - 1 - k} )}} \}^{2}}\end{matrix} & (12)\end{matrix}$

Yet another expression for the phase error can written as

$\begin{matrix}\begin{matrix}{{e_{phase}( {\Delta \; t} )} =} & { {\frac{1}{N}\sum\limits_{k = 1}^{N - 1}}\; \middle| {{y_{1}( {n - 1 - k} )} - {y_{2}( {n - 1 - k} )}} \middle| - } \\ & {| {{y_{2}( {n - 1 - k} )} - {y_{1}( {n - k} )}} |}\end{matrix} & (13)\end{matrix}$

or, alternatively,

$\begin{matrix}\begin{matrix}{{e_{phase}( {\Delta \; t} )} =} & { {\frac{1}{N}\sum\limits_{k = 0}^{N - 2}}\; \middle| {{y_{1}( {n - k} )} - {y_{2}( {n - k} )}} \middle| - } \\ & {| {{y_{2}( {n - k} )} - {y_{1}( {n - 1 - k} )}} |}\end{matrix} & (14)\end{matrix}$

Now look at the variation of the phase error with sampling time mismatchin different Nyquist zones. As an example, consider a sinusoidal signalof 90 MHz with a sampling frequency F_(S)=500 MHz. It can be noted thatthe input signal is in the first Nyquist zone. The spectrum of such asignal is shown in FIG. 1. In this spectrum is also seen a strong toneat 160 MHz. This is an image spur created due to sample-time mismatch.

For the sake of exposition, choose the phase error equationcharacterized by Eqn. 9. FIG. 2 shows the variation of e_(phase)(Δt)with Δt as a fraction of the sampling time of the TIADC for this signal.Next, consider a signal in the second Nyquist zone. For this, choose asinusoidal signal of 290 MHz with the same sampling frequency mentionedearlier. The spectrum of the aliased signal is shown in FIG. 3. Thestrong tone at 40 MHz is the image spur due to sample-time mismatch.

FIG. 4 shows the variation of e_(phase)(Δt) for the signal in the secondNyquist zone. As can be seen from FIG. 4, the slope of the phase erroris opposite to that of the phase error shown in FIG. 2.

Now assume an adaptive algorithm based on the sign of the phase error,viz., sign(e_(phase)(Δt)). Looking at FIG. 2, it can be seen that theadaptive algorithm will move to the right when sign(e_(phase)(Δt)) isnegative and move to the left when sign(e_(phase)(Δt)) is positive. Inthis way, the adaptive algorithm will converge to a timing mismatchvalue for which e_(phase)(Δt)≈0. Now apply this algorithm for the casewhen the input signal is in the second Nyquist zone.

From FIG. 4 it can also be seen that an adaptive algorithm will “move tothe right” when sign(e_(phase)(Δt)) is negative and move to the leftwhen sign(e_(phase)(Δt)) is positive. This results in divergence of thealgorithm. Thus, the adaptive algorithm should take into account theslope of the phase error. Towards this end, presented here is a methodof evaluating the slope of the phase error using a technique calledgradient (or slope) filtering.

Assume P values of e_(phase)(Δt_(k)) corresponding to Δt_(k) areavailable. Using the procedure from linear regression, one can fit aline through these points with an equation given by e_(p)=a+mΔt where ais the intercept given by

$\begin{matrix}{a = \frac{\begin{matrix}{{( {\sum_{k}\mspace{14mu} {e_{phase}\mspace{14mu} ( {\Delta \; t_{k}} )}} )( {\sum_{k}\mspace{14mu} {\Delta \mspace{14mu} t_{k}^{2}}} )} -} \\{( {\sum_{k}\mspace{14mu} {\Delta \mspace{14mu} t_{k}}} )( {\sum_{k}\mspace{14mu} {e_{phase}\mspace{14mu} ( {\Delta \; t_{k}} )\Delta \; t_{k}}} )}\end{matrix}}{{P( {\sum_{k}\mspace{14mu} {\Delta \mspace{14mu} t_{k}^{2}}} )} - ( {\sum_{k}\mspace{14mu} {\Delta \mspace{14mu} t_{k}}} )^{2}}} & (15)\end{matrix}$

and the slope m given by

$\begin{matrix}{m = \frac{\begin{matrix}{{P( {\sum_{k}\mspace{14mu} {e_{phase}\mspace{14mu} ( {\Delta \; t_{k}} )\Delta \; t_{k}}} )} -} \\{( {\sum_{k}\mspace{14mu} {\Delta \mspace{14mu} t_{k}}} )( {\sum_{k}\mspace{14mu} {e_{phase}\mspace{14mu} ( {\Delta \; t_{k}} )}} )}\end{matrix}}{{P( {\sum_{k}\mspace{14mu} {\Delta \mspace{14mu} t_{k}^{2}}} )} - ( {\sum_{k}\mspace{14mu} {\Delta \mspace{14mu} t_{k}}} )^{2}}} & (16)\end{matrix}$

It should be mentioned that what really is of interest here is the signof m since the direction of adaptation is controlled by it. Thus,irrespective of the Nyquist zone of the input signal, an adaptivealgorithm based on the product of sign(e_(phase)(Δt_(k))) and sign(m)will always converge.

By choosing an anti-symmetric distribution of Δt_(k) around zero,Σ_(k)Δt_(k)=0. Thus Eqn. 16 can be written as

$\begin{matrix}{m = \frac{\sum_{k}\mspace{14mu} {e_{phase}\mspace{14mu} ( {\Delta \; t_{k}} )\Delta \; t_{k}}}{\sum_{k}\mspace{14mu} {\Delta \mspace{14mu} t_{k}^{2}}}} & (17)\end{matrix}$

The denominator in the above equation is always positive and hence thesign of m can be written as

$\begin{matrix}{m_{s} = {{{sig}\; {n(m)}} = {{sig}\; {n( {\sum\limits_{k}\; {e_{phase}\mspace{14mu} ( {\Delta \; t_{k}} )\Delta \; t_{k}}} )}}}} & (18)\end{matrix}$

Therefore, knowing P ordered pair values of (e_(phase)(Δt_(k)), Δt_(k)),one can obtain the sign of m. If one chooses P to be odd,

$\begin{matrix}{{{\Delta \; t_{k}} = {k - \frac{P - 1}{2}}},{{{for}\mspace{14mu} k} = 0},1,\cdots,{P - 1}} & (19)\end{matrix}$

On the other hand if P is chosen to be even,

Δt _(k)=2k−(P−1), for k=0, 1, . . . , P−1  (20)

It can be noted that the values of Δt_(k) for both odd and even valuesof P are anti-symmetric and can thus form the coefficients of alinear-phase finite impulse response (FIR) filter. Consequently onlyhalf the values of Δt_(k) are sufficient to obtain the sign of m. Also,from a practical implementation perspective, the value of P should bekept small in order for the adaptive algorithm to quickly adjust tochanges in the sign of the phase error slope.

It is now possible to provide an adaptive algorithm based on the productof the signs of (e_(phase)(Δt_(k)) and m to compensate sample timemismatch errors.

Algorithm for Sample Time Mismatch

A simple schematic for a two-channel TIADC that implements sample-timecorrection is shown in FIG. 5. The clock circuitry 150 is such that twoADC cores, viz., ADC1-102-1 and ADC2 102-2, sample the input signal 101at F_(S)/2. In other words, for a clock running at F_(S), ADC1 102-1samples at odd sample clock instants (say) while ADC2-102-2 samples theinput signal 101 at even sample clock instants. The samples from ADC1102-1 and ADC2 102-2 are collected by a Digital Signal Processor (DSP)122 and the phase error is evaluated at regular intervals. The DSP 122then runs an adaptive algorithm determining the sign of the phase errorin conjunction with the sign of the gradient of the phase error to feeda Phase Look Up Table (LUT) 118 with a sample time correction input.

A block diagram that effects the adaptive algorithm in shown in FIG. 6.Generally speaking, the output of the adaptive algorithm forms theaddress to the Phase LUT (PLUT) 118. The output of the PLUT 118 thendirectly or indirectly provides the corresponding sample-time correctionto the clock and sample-time correction circuitry 150.

Assume the size of PLUT 118 to be N_(phase). If the maximum phasemismatch between the two ADCs 102-1, 102-2 is ±X_(p), then the entriesof the PLUT 118 will directly or indirectly cover the range [−X_(p),X_(p)] units. The distribution of the entries in PLUT 118 can be linear,logarithmic or based on any other distribution depending upon thecharacteristics of the analog circuits effecting the correction.

Let PLUT^(k) denote the address of PLUT 118 at the k^(th) iteration. Letμ^(k) denote a variable at the k^(th) iteration, and let μ_(phase) ^(k)denote a step size for the adaptive algorithm at the k^(th) iteration.Here, assume

μ_(phase) ^(k)ε[μ_(phasemin),μ_(phasemax)]  (21)

where μ_(phasemin) and μ_(phasemax) are the minimum and maximum values,respectively, of μ_(phase) ^(k). The adaptive algorithm for correctingthe phase error can thus be written as

$\begin{matrix}{{PLUT}^{k} = {N_{i} + \lfloor \mu^{k} \rfloor}} & (22) \\{\mu^{k + 1} = {\mu^{k} - {{sig}\; {n( {e_{phase}^{k}( {\Delta \; t} )} )}\mspace{14mu} {sig}\; {n( m_{s}^{k} )}\mu_{phase}^{k}}}} & (23) \\\begin{matrix}{\mu_{phase}^{k + 1} = {{\max ( {\frac{\mu_{phase}^{k}}{2},\mu_{phasemin}} )}\mspace{14mu} {if}\mspace{14mu} {mod}\mspace{14mu} ( {k,k_{p}} )}} \\{= 0}\end{matrix} & (24)\end{matrix}$

where N_(i) is the initial address of the PLUT (say N_(phase)/2), μ⁰=0,μ_(phase) ⁰=μ_(phase) and k_(p) is any arbitrary positive number.

The value of N_(i) also serves as a bias for the address input to thePLUT 118. Since the address of the PLUT ranges from 0 to N_(phase)−1,only positive values of are allowed. Thus μ^(k) can be negative orpositive while N_(i) is chosen such that PLUT^(k)ε[0 N_(phase)−1]. Itshould be mentioned that e_(phase) ^(k)(Δt) is evaluated using Eqn. 9and m_(s) ^(k) is evaluated using Eqn. 18. Since PLUT^(k) refers to anaddress of PLUT, the update happens only when μ^(k) changes by aninteger value in Eqn. 22. Consequently m_(s) ^(k) is also evaluated atsuch instants when μ^(k) changes by an integer value. At convergence,PLUT^(k) indicates the optimal address of PLUT that results in theminimum value of e_(phase)(Δt).

More particularly now, the algorithm uses the values e_(phase)(Δt_(k))202 and a running sum of the values of the slope m 203 (e.g.,e_(phase)(Δt_(k))Δt_(k)) as inputs. Next, a pair of sign blocks 204, 205determine the signs of the phase and slope of the phase. The signs aremultiplied (which can be implemented by XOR block 208) and themmultiplied 210 again by a Phase LUT step size amount, μ^(k).

This signal is then fed to a filter implemented by the sum block 212 anddelay 214. This arrangement provides a Finite Impulse Response (FIR)filter; it will be understood that other types of digital filters can beused, such as Infinite Impulse Response (IIR), combination FIR/IIR orother type of digital filters. A FIX block 216 then selects the integerpart (e.g., the fixed point part) of the floating point filter output.These integer values are then summed 218 with N_(i) to determine theinput address to the PLUT 118.

Experimental Results

Presented next are some experimental results based on the output of atwo-channel TIADC integrated circuit. In the first experiment, asinusoidal signal with a frequency of 90 MHz was used. The samplingfrequency of the two-channel TIADC system was 500 MHz. The adaptivealgorithm mentioned above was then run on the output of the two ADCs.

FIG. 7 shows the convergence of PLUT^(k) with iteration k, assumingN_(phase)=256 and P=5. As can be seen from the figure, the PLUT^(k)converges to a value between 127 and 128, which are the addressescorresponding to the vicinity of the minimum value of e_(phase)(Δt). Inorder to verify the convergence, it can be noted from FIG. 2 thate_(phase)(Δt) cross zero between 127 and 128. This confirms theconvergence of the adaptive algorithm.

In the second experiment, a sinusoidal signal with a frequency of 290MHz was used as the input. As can be noted, the input signal is in thesecond Nyquist zone. FIG. 8 shows the convergence of PLUT^(k) withiteration k. In this figure it can be seen that the algorithm divergesfirst before converging to the minimum value of e_(phase)(Δt), whichcorresponds to an address location of the PLUT between 122 and 123. Thereason for divergence is that it requires P values of e_(phase)(Δt)before the gradient of the phase error is evaluated. Once the slope isevaluated, the adaptive algorithm then moves in the correct direction toconverge. This convergence can be verified from FIG. 4 wheree_(phase)(Δt) crosses zero between these address values.

The robustness of this algorithm is seen when the input signal switchesNyquist zones. For this experiment, the input signal was a 90 MHz tonefor sometime and then switched to a 290 MHz tone. FIG. 9 shows theconvergence of PLUT^(k) with iteration k. It can be seen that thealgorithm settles to a PLUT address between 127 and 128 as long as theinput is a 90 MHz tone. When the input changes from 90 MHz tone to a 290MHz tone, the algorithm first moves in the wrong direction for a maximumof P points before it moves in the correct direction. This is because itneeds a maximum of P phase error values to evaluate the gradient of thephase error. Once the correct direction is established, the algorithmmoves towards the optimal address of PLUT, which is around 123. It canthus be seen that the adaptive algorithm is robust irrespective of theNyquist zone occupied by the input signal.

Use in a Digital System

The above teachings with respect to analog to digital converters havewide application in the filed of electronic devices and systems. Oneexample system is a digital signal transceiver. In such a system, thereceiver may include front end analog signal processing components suchas amplifiers, filters, and downconverters. A time interleaved analog todigital converter uses two or more subunit converters to provide adigital signal representative of the received signal(s) of interest.Digitizing the entire receive bandwidth of interest may require a veryhigh sampling rate; therefore, an interleaved system as described abovemay provide advantages over other conversion techniques.

FIG. 10 shows one such example transceiver system 1200 connected totransmit and receive a Radio Frequency (RF) signal. The RF signal may bea wireless signal received from an antenna or maybe received on a wiresuch as from a coaxial, optical fiber, or its like. The transceiver 1200transmits data to and receives data from a digital device 1211 such as acomputer, telephone, television, camera or any number of digitaldevices.

The transceiver 1200 shown in FIG. 10 uses a wideband, time-interleaved,analog-to-digital converter (ADC) 1206 as taught herein to digitizereceived signals. The output from the wideband ADC 1206 can be tuneddigitally, rather than with analog tuners, resulting in lower powerconsumption compared to alternative methods.

More particularly, in the example system 1200, signals are coupled via adiplexer 1202, which separates downstream (received) signals 1220 fromupstream (transmitted) signals 1222. The diplexer 1202 directs thereceived signal to a variable-gain amplifier (VGA) 1204, which amplifiesthe received signal before transmitting it through a filter 1205 to awideband ADC 1206. The time-interleaved ADC 1206 digitizes the receivedsignal, then passes the digitized signal 1240 to a digital tuner anddemodulator 1208. These demodulated signals may then be fed throughaccess control 1210 and then to a digital interface 1270.

A complete digital transceiver 1200 also typically includescorresponding transmit components such as modulator 1216, digital to aconverter 1218 and amplifier 1224. A CPU internal to the transceiver1200 may further control its operation. It should also be understoodthat other components not shown here, such as up converters and downconverters may form part of transceiver 1200.

Those of skill will further appreciate that the various illustrativecomponents, logical blocks, signal processing blocks, modules, circuits,and algorithm steps described in connection with the embodimentsdisclosed above may be implemented as analog or digital electronichardware, or as computer software, or as combinations of the same. Toclearly illustrate this interchangeability of hardware and software,various illustrative components, blocks, modules, circuits, and stepshave been described above generally in terms of their functionality.Whether such functionality is implemented as hardware or softwaredepends upon the particular application and design constraints imposedon the overall system. Those of skill in the art may implement thedescribed functionality in varying ways for each particular application,but such implementation decisions should not be interpreted as causing adeparture from the scope of the present invention.

The various illustrative components, logical blocks, modules, andcircuits described in connection with the embodiments disclosed hereinmay be implemented or performed with general purpose processors, digitalsignal processors (DSPs) or other logic devices, application specificintegrated circuits (ASICs), field programmable gate arrays (FPGAs),discrete gates or transistor logic, discrete hardware components, or anycombination thereof designed to perform the functions described herein.A general purpose processor may be any conventional processor,controller, microcontroller, state machine or the like. A processor mayalso be implemented as a combination of computing devices, e.g., acombination of a DSP and a microprocessor, a plurality ofmicroprocessors, one or more microprocessors in conjunction with a DSPcore, or any other such configuration.

The steps of the methods or algorithms described in connection with theembodiments disclosed herein may be embodied directly in hardware, insoftware or firmware modules executed by a processor, or in acombination thereof. A software product may reside in RAM memory, flashmemory, ROM memory, EPROM memory, EEPROM memory, registers, hard disk, aremovable disk, a CD-ROM, or any other form of storage medium known inthe art. An exemplary storage medium is coupled to the processor suchthe processor can read information from, and write information to, thestorage medium. In the alternative, the storage medium may be integralto the processor. The processor and the storage medium may reside in anASIC.

CONCLUSION

In this disclosure a robust method for correcting the phase error in atwo-channel TIADC system that is independent of the Nyquist zoneoccupied by the input signal has been described. The adaptive algorithmis based on estimating the gradient of the phase error using a filter.The coefficients of the filter can be derived from a simplifiedexpression of linear regression. The direction of the adaptation iscontrolled by the sign of the gradient. The adaptive algorithm convergesto the optimal value irrespective of the Nyquist zone occupied by theinput signal. The efficacy of the adaptive algorithm was shown by way ofexperimental results based on a two-channel TIADC.

The previous description of the disclosed embodiments is provided toenable any person skilled in the art to make or use the presentinvention. Various modifications to these embodiments will be readilyapparent to those skilled in the art, and the generic principles definedherein may be applied to other embodiments without departing from thespirit or scope of the invention. Thus, the present invention is notintended to be limited to the embodiments shown herein but is to beaccorded the widest scope consistent with the principles and novelfeatures disclosed herein.

While this invention has been particularly shown and described withreferences to example embodiments thereof, it will be understood bythose skilled in the art that various changes in form and details may bemade therein without departing from the scope of the inventionencompassed by the appended claims.

1. A method comprising: converting an input signal to provide to a setof two ADC outputs as first and second digital signals; estimating asample time error from the first and second digital signals; determininga correction signal from the sample time error regardless of a Nyquistzone occupied by the input signal; and applying the correction signal tothe converting step.
 2. The method of claim 1 wherein the determiningthe correction signal comprises estimating a gradient of the sample timeerror.
 3. The method of claim 2 wherein determining the correctionsignal further comprises determining a sign of the gradient of thesample time error.
 4. The method of claim 3 wherein determining thecorrection signal further comprises filtering the sign of the gradientof the sample time error.
 5. The method of claim 1 wherein the sampletime error is a digital value and the correction signal is an analogsignal.
 6. The method of claim 1 further comprising: locking up thecorrective signal in a stores value lookup table.
 7. The method of claim1 determining the correction sized from a value indicative of a Nyquistzone occupied by the input signal is determined from a gradient of thesample time error, and that value is then used in determining thecorrection signal.
 8. The method of claim 1 further comprising: storingcorrection values in a Phase Look Up Table (PLUT) wherePLUT^(k) = N_(i) + ⌊μ^(k)⌋μ^(k + 1) = μ^(k) − sig n(e_(phase)^(k)(Δ t))  sig n(m_(s)^(k))μ_(phase)^(k)$\begin{matrix}{\mu_{phase}^{k + 1} = {{\max ( {\frac{\mu_{phase}^{k}}{2},\mu_{phasemin}} )}\mspace{14mu} {if}\mspace{14mu} {mod}\mspace{14mu} ( {k,k_{p}} )}} \\{= 0}\end{matrix}$ such that N_(i) is an initial address offset of the PLUT,μ^(k) denotes a variable at the k^(th) iteration, and μ_(phase) ^(k)denotes a step size at the k^(th) iteration, μ_(phase) ⁰=μ_(phasemax),k_(p) is any arbitrary positive number, and e_(phase)(Δt_(k)) is anestimate of the phase error at iteration k.
 9. The method of claim 8further comprising: filtering an input to the PLUT.
 10. The method ofclaim 1 additionally comprising: interleaving the first and seconddigital signals to form a digital converter representation of the inputsignal.
 11. The method of claim 4 wherein the filtering step is a FiniteImpulse Response (FIR) filtering step.
 12. An apparatus comprising: twoor more Time-Interleaved Analog to Digital Converter (TIADC) cores,providing a set of two ADC outputs as first and second digital signals,at least one of the TIADC cores having a correction input; a signalinterleaver for combining the first and second digital signals to form adigital converted representation of the input signal; a digital signalprocessing operator, for estimating a phase error estimate from thefirst and second digital signals to provide a phase error estimate; anddetermining a correction signal from the phase error estimate regardlessof a Nyquist zone occupied by the input signal; and the correctionsignal being connected to the sample time correction input of at leastone of the TIADC cores.
 13. The apparatus of claim 12 additionallycomprising: a slope detector, for determining a slope of the phase errorestimate.
 14. The apparatus of claim 12 further comprising: a signoperation to determine a sign of the slop of the phase error estimate.15. The apparatus of claim 14 further comprising: a Finite ImpulseResponse (FIR) filter for filtering a sign of the gradient of the phaseerror.
 16. The apparatus of claim 12 wherein the phase error estimate isa digital value and the correction signal is an analog signal.
 17. Theapparatus of claim 12 additionally comprising a Look Up Table forproviding the correction signal.
 18. The apparatus of claim 12additionally wherein the connection value is determined by slopedetector further determining a value indicative of a Nyquist zoneoccupied by the input signal from a slope of the phase error estimate.19. The apparatus of claim 12 additionally comprising a Phase Look UpTable (PLUT) for determining the correction signal wherePLUT^(k) = N_(i) + ⌊μ^(k)⌋μ^(k + 1) = μ^(k) − sig n(e_(phase)^(k)(Δ t))  sig n(m_(s)^(k))μ_(phase)^(k)$\begin{matrix}{\mu_{phase}^{k + 1} = {{\max ( {\frac{\mu_{phase}^{k}}{2},\mu_{phasemin}} )}\mspace{14mu} {if}\mspace{14mu} {mod}\mspace{14mu} ( {k,k_{p}} )}} \\{= 0}\end{matrix}$ where N_(i) is an initial address offset of the PLUT,μ^(k) denotes a variable at the k^(th) iteration, and μ_(phase) ^(k)denotes a step size at the k^(th) iteration, μ_(phase) ⁰=μ_(phasemax),k_(p) is any arbitrary positive number, and e_(phase)(Δt_(k)) is anestimate of the phase error at iteration k.
 20. The apparatus of claim19 additionally comprising a filter for processing an input to the PLUT.21. A programmable computer product for use with a multiple channel timeinterleaved analog to digital converter, wherein first and seconddigital signals are interleaved to form a digital convertedrepresentation of an input signal, the product comprising one or moreprogrammable data processing machines that retrieve instructions from astored media and execute the instructions, the instructions for:receiving first and second digital signals; estimating a sample timeerror from the first and second digital signals; determining acorrection signal from the sample time error regardless of a Nyquistzone occupied by the input signal; and outputting the correction signal.22. A communication system comprising: a communication signal receiver,for receiving an input signal; an analog to digital converter (ADC)connected to the receiver, for producing a digital input signal; and ademodulator, for digitally demodulating the digitalized input signal;wherein the ADC further comprises: two or more time interleaved ADCcores, providing at least first and second digital signals, at least oneADC core having a correction input; is a digital signal processingoperation for: determining a phase error estimate from the first andsecond digital signals; and producing a correction signal from the phaseerror estimate regardless of any Nyquist zone(s) occupied by the firstand second digital signals.